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A046147 Triangle read by rows in which row n lists the primitive roots mod n (omitting numbers n without a primitive root). 5
1, 2, 3, 2, 3, 5, 3, 5, 2, 5, 3, 7, 2, 6, 7, 8, 2, 6, 7, 11, 3, 5, 3, 5, 6, 7, 10, 11, 12, 14, 5, 11, 2, 3, 10, 13, 14, 15, 7, 13, 17, 19, 5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 2, 3, 8, 12, 13, 17, 22, 23, 7, 11, 15, 19, 2, 5, 11, 14, 20, 23, 2, 3, 8, 10, 11, 14, 15, 18, 19, 21, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

T. D. Noe, Table of n, a(n) for n = 2..3119 (first 99 nonempty rows of triangle, flattened)

Eric Weisstein's World of Mathematics, Primitive Root.

EXAMPLE

n followed by primitive roots, if any:

1 -

2 1

3 2

4 3

5 2 3

6 5

7 3 5

8 -

9 2 5

10 3 7

11 2 6 7 8

12 -

13 2 6 7 11

...

MAPLE

f:= proc(n) local p, k, m, R;

     p:= numtheory:-primroot(n);

     if p = FAIL then return NULL fi;

     m:= numtheory:-phi(n);

     k:= select(i -> igcd(i, m) = 1, [$1..m-1]);

     op(sort(map(t -> p&^t mod n, k)))

end proc:

f(2):= 1:

map(f, [$2..50]); # Robert Israel, Apr 28 2017

MATHEMATICA

a[n_] := Select[Range[n-1], GCD[#, n] == 1 && MultiplicativeOrder[#, n] == EulerPhi[n]& ]; Table[a[n], {n, 1, 30}] // Flatten (* Jean-Fran├žois Alcover, Oct 23 2012 *)

PrimitiveRootList[Range[Prime[10]]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 10 2016 *)

CROSSREFS

Cf. A001918, A046144, A046145, A046146.

Cf. A060749

Sequence in context: A124459 A283360 A256366 * A251865 A052369 A110976

Adjacent sequences:  A046144 A046145 A046146 * A046148 A046149 A046150

KEYWORD

nonn,tabf

AUTHOR

Eric W. Weisstein

EXTENSIONS

Edited by Robert Israel, Apr 28 2017

STATUS

approved

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Last modified May 26 03:36 EDT 2017. Contains 287073 sequences.